Solve for $x$ : $5x^2 + 55x + 150 = 0$
Solution: Dividing both sides by $5$ gives: $ x^2 + {11}x + {30} = 0 $ The coefficient on the $x$ term is $11$ and the constant term is $30$ , so we need to find two numbers that add up to $11$ and multiply to $30$ The two numbers $6$ and $5$ satisfy both conditions: $ {6} + {5} = {11} $ $ {6} \times {5} = {30} $ $(x + {6}) (x + {5}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 6) (x + 5) = 0$ $x + 6 = 0$ or $x + 5 = 0$ Thus, $x = -6$ and $x = -5$ are the solutions.